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M. Stanishkov

Publications and source records attributed to M. Stanishkov.

17 recordsLinked to original sources
arXiv2026

Four-point functions with fractional R-symmetry excitations in the D1-D5 CFT

We study correlation functions with fractional-mode excitations of the R-symmetry currents in D1-D5 CFT. We show how fractional-mode excitations lift to the covering surface associated with correlation functions as a specific sum of integer-mode excitations, with coefficients that can be determined exactly from the covering map in terms of Bell polynomials. We consider the four-point functions of fractional excitations of two chiral/anti-chiral NS fields, Ramond ground states and the twist-two scalar modulus deformation operator that drives the CFT away from the free point. We derive explicit formulas for classes of these functions with twist structures $(n)$-$(2)$-$(2)$-$(n)$ and $(n_1)(n_2)$-$(2)$-$(2)$-$(n_1)(n_2)$, the latter involving double-cycle fields. The final answer for the four-point functions always depends only on the lift of the base-space cross-ratio. We discuss how this relates to Hurwitz blocks associated with different conjugacy classes of permutations, the corresponding OPE channels and fusion rules.

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arXiv2022

Four-point functions with multi-cycle fields in symmetric orbifolds and the D1-D5 CFT

We study $S_N$-invariant four-point functions with two generic multi-cycle fields and two twist-2 fields, at the free orbifold point of the D1-D5 CFT. We derive the explicit factorization of these functions following from the action of the symmetric group on the composite multi-cycle fields. Apart from non-trivial symmetry factors that we compute, the function with multi-cycle operators is reduced to a sum of connected correlators in which the composite fields have, at most, two cycles. The correlators with two double-cycle and two single-cycle fields give the leading order contribution in the large-$N$ limit. We derive explicit formulas for these functions, encompassing a large class of choices for the single- and the double-cycle fields, including generic Ramond ground states, NS chiral fields and the marginal deformation operator. We are thus able to extract important dynamical information from the short-distance OPEs: conformal dimensions, R-charges and structure constants of families of BPS and non-BPS fields present in the corresponding light-light and heavy-light channels. We also discuss properties of generic multi-cycle $Q$-point functions in $M^N/S_N$ orbifolds, using a technology due to Pakman, Rastelli and Razamat.

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arXiv2021

Dynamics of R-neutral Ramond fields in the D1-D5 SCFT

We describe the effect of the marginal deformation of the $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ orbifold theory on a doublet of R-neutral twisted Ramond fields, in the large-$N$ approximation. Our analysis of their dynamics explores the explicit analytic form of the genus-zero four-point function involving two R-neutral Ramond fields and two deformation operators. We compute this correlation function with two different approaches: the Lunin-Mathur path-integral technique and the stress-tensor method. From its short distance limits, we extract the OPE structure constants and the scaling dimensions of non-BPS fields appearing in the fusion. In the deformed CFT, at second order in the deformation parameter, the two-point function of the $n$-twisted Ramond fields is UV-divergent. We perform an appropriate regularization, together with a renormalization of the undeformed fields, obtaining finite, well-defined corrections to their two-point functions and their bare conformal weights, for $n < N$. The fields with maximal twist $n=N$ remain protected from renormalization, with vanishing anomalous dimensions.

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arXiv2021

On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT

We examine the behavior of the Ramond ground states in the D1-D5 CFT after a deformation of the free-orbifold sigma model on target space $({\mathbb T}^4)^N / S_N$ by a marginal interaction operator. These states are compositions of Ramond ground states of the twisted and untwisted sectors. They are characterized by a conjugacy class of $S_N$ and by the set of their "spins", including both R-charge and "internal" SU(2) charge. We compute the four-point functions of an arbitrary Ramond ground state with its conjugate and two interaction operators, for genus-zero covering surfaces representing the leading orders in the large-$N$ expansion. We examine short distance limits of these four-point functions, shedding light on the dynamics of the interacting theory. We find the OPEs and a collection of structure constants of the ground states with the interaction operators and a set of resulting non-BPS twisted operators. We also calculate the integrals of the four-point functions over the positions of the interaction operators and show that they vanish. This provides an explicit demonstration that the Ramond ground states remain protected against deformations away of the free orbifold point, as expected from algebraic considerations using the spectral flow of the ${\mathcal N} = (4,4)$ superconformal algebra with central charge $c = 6N$.

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arXiv2021

Renormalization of Twisted Ramond Fields in D1-D5 SCFT$_2$

We explore the Ramond sector of the deformed two-dimensional $\cal N = (4, 4)$ superconformal $(T^4)^N /S_N$ orbifold theory, describing bound states of D1-D5 brane system in type IIB superstring. We derive the large-$N$ limit of the four-point function of two R-charged twisted Ramond fields and two marginal deformation operators at the free orbifold point. Specific short-distance limits of this function provide several structure constants, the OPE fusion rules and the conformal dimensions of a few non-BPS operators. The second order correction (in the deformation parameter) to the two-point function of the Ramond fields, defined as double integrals over this four-point function, turns out to be UV-divergent, requiring an appropriate renormalization of the fields. We calculate the corrections to the conformal dimensions of the twisted Ramond ground states at the large-$N$ limit. The same integral yields the first-order deviation from zero of the structure constant of the three-point function of two Ramond fields and one deformation operator. Similar results concerning the correction to the two-point function of bare twist operators and their renormalization are also obtained.

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arXiv2020

Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT$_2$

We study two families of composite twisted Ramond fields (made by products of two operators) in the $\cal {N}=(4,4)$ supersymmetric D1-D5 SCFT$_2$ deformed by a marginal modulus operator away from its $(T^4)^N/ S_N$ free orbifold point. We construct the large-$N$ contributions to the four-point functions with two composite operators and two deformation fields. These functions allow us to derive short-distance OPE limits and to calculate the anomalous dimensions of the composite operators. We demonstrate that one can distinguish two sets of composite Ramond states with twists $m_1$ and $m_2$: protected states, for which $m_1+m_2=N$, and "lifted" states for which $m_1+m_2<N$. The latter require an appropriate renormalisation. We also derive the leading order corrections to their two-point functions, and to their three-point functions with the deformation operator.

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arXiv2020

Microstate Renormalization in Deformed D1-D5 SCFT

We derive the corrections to the conformal dimensions of twisted Ramond ground states in the deformed two-dimensional $\mathcal N = (4,4)$ superconformal $(\mathbb T^4)^N/S_N$ orbifold theory describing bound states of the D1-D5 brane system in type IIB superstring theory. Our result holds to second order in the deformation parameter, and at the large $N$ planar limit. The method of calculation involves the analytic evaluation of integrals of four-point functions of two R-charged twisted Ramond fields and two marginal deformation operators. We also calculate the deviation from zero, at first order in the considered marginal perturbation, of the structure constant of the three-point function of two Ramond fields and one deformation operator.

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arXiv2012

On the semiclassical 3-point function in AdS_3

We reconsider the problem of determining the semiclassical 3-point function in the Euclidean AdS_3 model. Exploiting the affine symmetry of the model we use solutions of the classical Knizhnik-Zamolodchikov (KZ) equation to compute the saddle point of the action in the presence of three vertex operators. This alternative derivation reproduces the "heavy charge" classical limit of the quantum 3-point correlator. It is different from the recently proposed expression obtained by generalised Pohlmeyer reduction in AdS_2

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arXiv2010

Three-point correlation functions in N=1 Super Lioville Theory

In this letter we propose exact three-point correlation functions for N=1 supersymmetric Liouville theory. Along the lines of Zamolodchikov and Zamolodchikov paper (hep-th/9506136) we propose a generalized special function which describe the three-point amplitudes. We consider briefly the so called reflection amplitudes in the supersymmetric case.

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arXiv2008

Non-critical string pentagon equations and their solutions

We derive pentagon type relations for the 3-point boundary tachyon correlation functions in the non-critical open string theory with generic c_{matter} < 1 and study their solutions in the case of FZZ branes. A new general formula for the Liouville 3-point factor is derived.

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arXiv2002

Duality in N=2 Super-Liouville Theory

In this paper we consider a strong-weak coupling duality of the N=2 super-Liouville field theory (SLFT). Without the self-duality found in other Liouville theories, the N=2 SLFT, we claim, is associated with a `dual' action by a transformation $b\to 1/b$ where $b$ is the coupling constant. To justify our conjecture, we compute the reflection amplitudes (or two-point functions) of the (NS) and the (R) operators of the N=2 SLFT based on the conjectured dual action and show that the results are consistent with known results.

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arXiv2001

Expectation values of descendent fields in the Bullough-Dodd model and related perturbed conformal field theories

The exact vacuum expectation values of the second level descendent fields $<(\partialϕ)^2({\overline\partial}ϕ)^2e^{aϕ}>$ in the Bullough-Dodd model are calculated. By performing quantum group restrictions, we obtain $ $ in the $Φ_{12}$, $Φ_{21}$ and $Φ_{15}$ perturbed minimal CFTs. In particular, the exact expectation value $ $ is found to be proportional to the square of the bulk free energy.

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arXiv2000

Hidden Virasoro Symmetry of (Soliton Solutions of) the Sine Gordon Theory

We present a construction of a Virasoro symmetry of the sine-Gordon (SG) theory. It is a dynamical one and has nothing to do with the space-time Virasoro symmetry of 2D CFT. Although it is clear how it can be realized dyrectly in the SG field theory, we are rather concerned here with the corresponding N-soliton solutions. We present explicit expressions for their infinithesimal transformations and show that they are local in this case. Some preliminary stages about the quantization of the classical results presented in this paper are also given.

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arXiv1998

On the Null Vectors in the Spectra of the 2D Integrable Hierarchies

We propose an alternative description of the spectrum of local fields in the classical limit of the integrable quantum field theories. It is close to similar constructions used in the geometrical treatment of W-gravities. Our approach provides a systematic way of deriving the null-vectors that appear in this construction. We present explicit results for the case of the A_1^{1}-(m)KdV and the A_2^{2}-(m)KdV hierarchies, different classical limits of 2D CFT's. In the former case our results coincide with the classical limit of the construction of Babelon, Bernard and Smirnov.Some hints about quantization and off-critical treatment are also given.

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arXiv1994

Integrable perturbations of CFT with complex parameter: the $M_{3/5}$ model and its generalizations

We give evidence, by use of the Thermodynamic Bethe Ansatz approach, of the existence of both massive and massless behaviours for the $ϕ_{2,1}$ perturbation of the $M_{3,5}$ non-unitary minimal model, thus resolving apparent contradictions in the previous literature. The two behaviours correspond to changing the perturbing bare coupling constant from real values to imaginary ones. Generalizations of this picture to the whole class of non-unitary minimal models $M_{p,2p\pm 1}$, perturbed by their least relevant operator lead to a cascade of flows similar to that of unitary minimal models perturbed by $ϕ_{1,3}$. Various aspects and generalizations of this phenomenon and the links with the Izergin-Korepin model are discussed.

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arXiv1993

Off critical current algebras

We discuss the infinite dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis in the structure of the consequent non-abelian infinite dimensional algebra generalizing $W_\infty$ to the case of a non abelian group. We prove that the pure left-symmetry as well as the pure right-sector of the thus obtained algebra coincides with the conformally invariant case. The mixed sector is more involved, although the general structure seems to be near to be unraveled. We also find some subalgebras that correspond to Kac-Moody algebras. The constraints imposed by the algebras are very strong, and in the case of the massive deformation of a non-abelian fermionic model, the symmetry alone is enough to fix the 2- and 3-point functions of the theory.

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